From the air, the Museum aan de Stroom in Antwerp looks like a stack of red Lego bricks. Large, expensive Lego bricks, dropped by some tired giant child and stuck together with what could conceivably be great swathes of Sellotape. The city's newest museum, designed by the Dutch architects Willem Jan Neutelings and Michiel Riedijk opened this month and looks more solid but no less fanciful from the ground. The Sellotape is in fact wide panels of undulating glass separating 10 giant stone containers, stacked one on top of the other and clad in violent red Indian sandstone.

It's an idiosyncratic design that contrasts with the city's predominant architectural styles – the traditional Flemish ziggurat roofs of the pretty historic centre and the port's brutalist industrial sprawl. But this is exactly the point: Museum aan de Stroom (which is known as MAS and translates as Museum by the River) is intended to be a bridge between the city centre and the port.

This is meant both literally and metaphorically: the museum is in a dockside area called Het Eilandje (the little island) sitting between the two, and it contains more than 470,000 exhibits relating to the history of Antwerp's port and its people.

It's not just the exhibitions and architecture that will draw the crowds; on MAS's top floor is 't Zilte (tzilte.be), a double Michelin-starred restaurant which has just moved here from Mol, a small town nearby. Here, chef Viki Geunes serves creative haute cuisine – including poulet de Bresse with shiitake mushrooms, a prawn mousse with foie gras that is presented in a glass ball, and his award-winning dame blanche dessert, a sort of skilfully deconstructed choc ice. There is a six-week waiting list for a table.

Inside the Museum aan de Stroom. Photograph: Filip Dujardin

The museum's exhibitions are laid out thematically, floor by floor. The Visible Storage section on the second floor is particularly absorbing: here, you get a rare chance to see the thousands of objects that would be hidden away in storage in other museums. I opened drawers at random to find armoured breastplates lying alongside a set of intricately carved ivory Madonnas; it was like having the run of some brilliantly eccentric collector's back room.

The first temporary exhibition, Masterpieces in the MAS, runs until 30 December and features artworks produced in or near Antwerp over the past four centuries – from paintings by Peter Paul Rubens and Jan van Eyck to contemporary pieces by Flemish artists such as Jan Fabre, who makes oddly appealing sculptures out of insect carapaces.

Those who can't afford the Michelin-starred food should at least visit the ninth floor's spectacular terrace: it has amazing views across the city, the port and the river Scheldt. It's free to get up here (entry to the exhibitions costs up to €10), though you're likely to share it with restaurant diners sipping pricey aperitifs. There's a more affordable cafe, Storm, on the ground floor.

MAS is a clear indicator that Het Eilandje has finally completed its transition from neglected dockside to fashionable district. This regeneration has been masterminded by the city council and propelled by its decision, 10 years ago, to build the museum here in an area dubbed "Siberia" by locals because it takes a good half-hour to walk here from the centre.

The docks were constructed for Napoleon in 1811, as a base for his planned naval invasion of London, but by the middle of the last century had fallen into disrepair. The whole Het Eilandje area – which includes Antwerp's two oldest docks, Bonaparte and Willem, and a grid of streets stretching between the red light district and the main harbour – has undergone massive reconstruction and is now a lovely place for a stroll.

Most tourists come to Antwerp to stock up on chocolate, beer or diamonds (the city is one of the biggest diamond markets in the world) or to test its reputation as Belgium's funky hub for fashion and design. But Het Eilandje is another good reason to make the trip. Yachts and sailboats bob prettily in Willemdok; there's a line of trendy bars and restaurants opposite MAS; and a few blocks away is the Felix Pakhuis (Godefriduskaai 30, +32 3 203 0330, felixpakhuis.nu), a meticulously restored warehouse that now houses the city's national archive and another artfully minimalist fusion restaurant where you can eat tandoori chicken while sitting out by the water.

The fashion designer Dries Van Noten has just moved his atelier to another warehouse conversion next door; and just round the corner is Marcel (Van Schoonbekeplein 13, +32 3 336 3302, restaurantmarcel.be), an excellent bistro housed in a former American presbyterian church. Its beige walls, brass bar and sanded floors lend it an elegant, Parisian feel.

So far, so gentrified – but much of Het Eilandje feels like it's still holding its breath. The upper floors of many of the apartment buildings are plastered with adverts for luxury loft conversions, but most of them still appear to be empty. I pass one front door, left hanging open on its hinges, and see that it leads on to a dank-smelling front room piled with old blankets and mattresses.

But with the opening of the MAS and several major construction projects planned – including the complete remodelling of several of the ugly high-rises and overly trafficked streets, and a new Zaha Hadid-designed port authority headquarters at the mouth of the harbour, surmounted by a huge glass diamond – the area is soon sure to lose its forgotten, industrial feel.

The Royal Ballet of Flanders recently moved into a new corrugated-iron headquarters on the corner of Kattendijkdok and Westkaai, next to a dilapidated, semi-roofless building from which millions of emigrants once left for America aboard Red Star Line ships. A museum dedicated to the Red Star Line will open here in 2012.

And a 20-minute walk from MAS there is another renowned restaurant, Het Pomphuis (Siberiastraat z/n, +32 3 770 8625, hetpomphuis.be), set in a former dry-dock pumping station. The three-storey building is spectacular: in the basement stand the three huge iron pumps that could once empty the neighbouring dry dock in two hours; while upstairs, under the soaring glass roof, you can enjoy a cocktail and some fantastic fish dishes, which range from lobster to yellowfin tuna and cod stew.

Food, art and culture can all be found in Het Eilandje, but there's nowhere in the area to stay just yet, apart from a Holiday Inn Express on Italiëlei, a busy main road. Happily, there are dozens of gorgeous boutique hotels and B&Bs in the city centre, such as Boulevard Leopold (+32 3 225 5218, boulevard-leopold.be; doubles from €110 B&B).

The other thing the area lacks, at least for now, is decent shopping. However, Antwerp is renowned for its fashion and design, so this is bound to change – but apart from the MAS shop, which sells a good selection of hefty tomes on art, photography and fashion, I found just one (excellent) travel bookshop, Alta Via (Nassaustraat 29, +32 3 293 8733, altaviatravelbooks.be), which owner Xavier Lietaer has lovingly constructed entirely out of recycled materials, and one rather lonely boutique, Y di Cassanova (Westkaai 45), selling frilly knickers out of the ground floor of a tower block.

Its other shops veer between expensive retailers of flooring and bathrooms clearly aimed at prospective loft owners and dark little places selling fire extinguishers and barometers and sou'westers and anything else you might need for life aboard an oil tanker.

Places like this are sure to disappear soon – so it's worth taking your time to stroll around Het Eilandje and commit to memory a place that, within five years, is likely to have been completely transformed. As an area in transition, it is fascinating.

•To get to Antwerp by train, take the Eurostar from London to Brussels (two hours), and from there it is 40 minutes by train to Antwerp Centraal station. Rail Europe has returns from £80 (0844 848 4064, raileurope.co.uk). For further information, see mas.be and Tourism Flanders-Brussels (020-7307 7738, visitflanders.co.uk)